Intrigued by this empirical result, we computed numerical values for
several of these and similar sums, which we have termed Euler sums.
We then analyzed these values by a technique we will present below
that permits one to determine, with a high level of confidence,
whether a numerical value can be expressed as a rational linear
combination of several given constants. These efforts produced even
more empirical evaluations, suggesting broad patterns and general
conjectures. Ultimately proofs were found for many of these
experimental results.
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